I`m considering several models such as GLM, GLMM, zero-inflated, and zero-inflated mixed in the count data.
All my work was done in R.
Prior studies confirmed that there is a problem of zero excess and over-dispersion as a consideration in counter data analysis.
So I tried the following tests.
1. zero excess
Voung test was performed using the zero-inflated model and the GLM.
Vuong of the pscl package was used.
- ZIP vs. GLM Poisson
- ZINB vs. GLM NB
Significant results were obtained from the above two tests (p<0.05).
2. over-dispersion
dispersion test was performed to find out why over-dispersion should be
considered in real data using the Poisson model.
dispersiontest of the AER package was used (Cameron, A.C. and Trivedi 1990).
The above test results in rejection of the null hypothesis (p<0.05)
In addition, it was confirmed that dispersion parameter(1/theta) had a value of about 0.39.
However, I have not yet found a verification method for the reason why random effects should be considered.
My data is traffic accident data according to the year of each road. i.e. it is longitudinal count data.
I was told by a professor of statistics that a mixed model should be used considering road heterogeneity.
Therefore, I constructed GLMM poisson/NB and zero-inflated mixed poisson/NB using random effects by road and confirmed the results.
GLMM used glmer of lme4, and glmmTMB of glmmTMB was used as the zero-inflated mixed model.
I did the Houseman test at first. However, this test compares the fixed-effects model with the random-effects model and was considered inappropriate for the count data (not linear model).
Crucially, when testing the random effect of the mixed model from the count data, no previous study was seen that conducted the Hausmann test.
Therefore, my question is as follows:
1. I would like to know if there is a previous study that identifies the reason for considering ramdom effect in modeling in longitudinal study data.
2. Is there a validation method to verify the significant effects of random effects in the mixed model?
- The AIC and BIC comparison has already been carried out.
3. If there is a way, what package does R use? Additionally, how to use it